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Applying the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.

If two angles are alternate interior angles formed along a transversal on two parallel lines, then their measures are congruent or the same.

Angles on a straight line are angles that lie along a straight line, and the sum of the angles equals 180 degrees.

Given the following:

m∠BFC = 75°

m∠GFC = 38°

∠EFB, ∠BFC,  and ∠GFC are angles on a straight line, therefore:

m∠EFB = 180 - m∠BFC - m∠GFC

Plug in the values

m∠EFB = 180 - 75 - 38

m∠EFB = 67°

Find the measure of angle FBC:

Angles FBC and EFB are alternate interior angles, therefore:

m∠FBC = m∠EFB = 67° [alternate interior angles theorem]

m∠FBC = 67°

In summary, using the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.

Answer:

27

Step-by-step explanation:

factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

factors of 27 = 1, 3, 9, 27

The greatest factor that exactly divides both 54 and 27 is  27 because they both have it as a factor.

Answer:

A. F(x)=

Step-by-step explanation:

The graph below represents the rational function F(x)= 10. This can be seen by the fact that the vertical asymptote of the graph is located at x = 0, indicating that the denominator of the fraction is equal to 10.

The solution of the equation [tex]\rm 9^y = 3*6*27*4*81*2[/tex] will be 5.76.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

[tex]\rm 9^y = 3*6*27*4*81*2[/tex]

Simplify the equation, then the value of the variable 'y' will be given as,

[tex]\rm 9^y = 3*6*27*4*81*2\\\\9^y = 314,928[/tex]

Take log on both sides, then we have

y log 9 = log 314,928

0.9542 y = 5.4782

y = 5.76

The solution of the equation [tex]\rm 9^y = 3*6*27*4*81*2[/tex] will be 5.76.

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The scientific notation of the decimal number 0.0005682 is 5.682×10⁻⁴

A number system is defined as a system of writing to express numbers.

The given decimal number is 0.0005682.

We need to convert to the scientific notation.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The decimal number 0.0005682 is too small. So we are converting it to the scientific notation.

If we take the decimal value to the right side of 5.

Then scientific notation of  0.0005682 is 5.682×10⁻⁴.

Hence,  5.682×10⁻⁴ is the scientific notation of the decimal number 0.0005682.

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Answer:

[tex]120^{\circ}, 120^{\circ}, 60^{\circ}, 60^{\circ}[/tex]

Step-by-step explanation:

The angles of a quadrilateral add to [tex]360^{\circ}[/tex].

[tex]2h+2h+h+h=360 \\ \\ 6h=360 \\ \\ h=60 \implies 2h=120[/tex]

Answer:

It is given :

Now,

3x + 4x = 56

7x = 56

x = 8

Now,

So, there are 32 black cats and 24 white cats.

Answer:

y = 3x + 72

Step-by-step explanation:

To solve for y, we can rearrange the equation to the form y = 3x + b, where b is a constant. To do this, we move the -9y to the left side of the equation and the 3x to the right side, which gives us -9y - 3x = 81. We can then divide both sides by -9, which gives us y = 3x + 72.

Answer:

2/35

Step-by-step explanation:

[tex]\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}[/tex]

Answer:

See below

Step-by-step explanation:

Desmos is a free graphing calculator.

Answer:B

manning the phone banks during a broadcast

Step-by-step explanation:

Answer: B: manning the phone banks during a broadcast

k12 test career

Correlation may not always indicate causality shown below.

What do you mean by corelation and causation?

We can determine how strongly a pair of variables are linearly associated and change together using the statistical technique of correlation. It only states that there is a relationship; it doesn't explain why or how it came to be. Correlation goes one step farther than causality. It states that any change in one variable's value will result in a change in another variable's value, or that one variable causes the occurrence of another. It also goes by the name "cause and effect."

may not always indicate causality. with a well-known instance.

In New York, ice cream sales and homicide rates are associated (Study)

The frequency of homicides fluctuates along with ice cream sales. Does ice cream consumption result in deaths of people?

No. The mere correlation of two events does not imply causation.

Since correlation does not imply causation in our example, ice cream is not to blame for any fatalities.

There are occasionally some unspoken aspects that are somehow connected. Weather is the underlying factor that drives both ice cream sales and homicide rates, as in our example. The increase in ice cream sales and killings is actually a result of the weather.

Therefore, significant linear correlation does not imply causality.

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Answer: 2/5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First, you have to find the unit rate. Since you know that 2 pounds cost $5.04, you can divide the cost by 2 to find out how much 1 pound costs which would equal 2.52. Hope that helps.

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

What is system of equations?

A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.

Given:

Juan's school is selling tickets to the annual talent show.

On the first day of ticket sales the school sold 6 adult tickets and 3 student tickets for a total of $51.

The school took in $90 on the second day by selling 9 adult tickets and 6 student tickets.

Let A be the number of adult tickets sold.

S be the number of students ticket sold.

⇒ 6A + 3S = $51            ..(1)

9A + 6S = $90              ..(2)

Multiply first equation by (2)

12A + 6S = $102            ..(3)

Subtract equation (2) and (3)

   12A + 6S = $102

-   9A + 6S = $90

________________

   3A        = 12

⇒ A = $4

Plug A = 4 in equation (1)

6(4) + 3S = $51

24 + 3S = $51

3S = $51 - $24

3S = $27

S = $9

Hence,

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

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Answer:

------------------------------

Let side length be s.

We know the area of the square is 100 cm².

Use the equation for the area and find the value of s:

Answer: Reflection over x-Axis

Step-by-step explanation:

Using percentages we can conclude that Amanda achieved 77.34% of her goal.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without dimensions and without a standard measurement.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

So, percent of goals Amanda achieved:

She exercised for 58 minutes.

Then,

58/75 * 100

77.34%

Therefore, using percentages we can conclude that Amanda achieved 77.34% of her goal.

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Correct question:
A 6th-grade class did a weekend fitness challenge. Each student set a goal of `75` minutes of fitness. Amanda exercised for `58` minutes. What percent of the goal did she achieve?

The value of c is a real solution to the equation [tex]4x^{2}-8x +c[/tex] = 0 is 4

In algebra, a "real solution" is any answer to an equation that is a real number.

There is just one true solution where discriminant b2 - 4ac equals zero. The equation x2 + 2x + 1 = 0 has one solution, x = -1.

Depending on whether the discriminant is positive, zero, or negative, there are many answers to the quadratic equation that has been presented.

A positive discriminant indicates that the quadratic has two distinct real number solutions.

A discriminant of zero indicates that the quadratic equation has a repeating real number solution.

The quadratic equation given is

[tex]4x^{2}-8x +c[/tex] = 0

For real solution

Discriminant = 0

[tex]b^{2}-4ac[/tex] = 0

[tex]8^{2}-4(4)(c)[/tex] = 0

64 - 16c = 0

-16c = -64

c = 4

The value of c is a real solution to the equation [tex]4x^{2}-8x +c[/tex] = 0 is 4

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Graph C represents the equation y = x + 5.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Let the equation be y = x + 5

The values of m = 1 and b = 5

The slope of the line exists the value of [tex]$$m_r$[/tex] and the y-intercept exists the value of b.

Slope: 1 and y-intercept: (0, 5)

Any line can be graphed utilizing two points. Select two x values, and plug them into the equation to estimate the corresponding y values.

Create a table of the x and y values.

x           y

0          5

1           6

Graph the line utilizing the slope and the y-intercept, or the points.

Slope: 1

Therefore, the correct answer is option b) Graph C.

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Answer: 22 & 15

Step-by-step explanation:

Let the number be x

Other number=x-7

x+(x-7)=37

x+x-7=37

2x=37+7

2x=44

x=44/2

x=22

22 - 15 = 7              -------has difference of 7

x=22 + 15 = 37

Therefore, 22 is the first number & 15 is the second.

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

The line of symmetry for the given figure is (B) 1, 2, and 3.

A line of symmetry divides a form or item into two equal and symmetrical parts.

We also refer to this line as the axis of symmetry or the mirror line since it divides the figure symmetrically and the divided areas resemble mirror copies of one another.

A regular polygon is a square.

It has four sides and four lines of symmetry.

Regular pentagons have five sides and five symmetry lines. In a regular polygon, the number of symmetry lines equals the number of sides.

So, according to the given figure:

All lines 1, 2, and 3 after diving the figure and leaving the figure with 2 identical parts.

Therefore, the line of symmetry for the given figure is (B) 1, 2, and 3.

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Answer:

x  ≤ 2 1/2 (Option 2)

Step-by-step explanation:

Multiply both sides of the equation by 2, which gives us 7 ≥ 2.8x. Swap the sides so all variables on on the left. Divide both sides by 2.8, which gives us the fraction 7/2.8. Multiply both numbers by 10 to get 70/28. Reduce to lowest terms.

Answer:

884.4

Step-by-step explanation:

Answer:

The original price is 895.12$

I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this

Step-by-step explanation:

The experiment is the development of a new soft drink

From the question, we understand that:

The Fresno Mall plans to survey teenagers about a newly developed soft drink

This implies that the experiment is the survey of teenagers for a new soft drink

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one outcome could be "Prefer this new drink"

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one event could be "The event that 5 of 10 teenagers prefer this new drink to their favourite drink"

Using the question as a guide, a survey could be:

In a survey of 500 randomly selected adults, 68% of the respondents think that the government should require parents to have their children vaccinated.

Here, we have:

Probabilities, in this scenario are used to determine the proportions of outcomes, events and it is used to make informed decisions

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Answer:

Hope this helps

Step-by-step explanation:

The angle formed by the two cables is approximately 59.1 degrees.

Answer:

length = 8 yds

width = 5.5 yds

Step-by-step explanation:

Area of rectangle = l * w

w = width

length = 2w - 3

Substitute l with 2w - 3:

(2w - 3)*w = 44

2w² - 3w = 44

2w² - 3w - 44 = 0

Solve for w (AC method):

2w² + 8w - 11w - 44 = 0

2w(w + 4) - 11(w + 4) = 0

(2w - 11)(w + 4) = 0

w = 5.5 or w = -4

note: length cannot be negative, so w = 5.5 yds

Substitute w with 5.5 in either equation:

5.5 * l = 44 yds²

l = 44/5.5 = 8 yds

or

l = 2(5.5) - 3

l = 11 - 3 = 8 yds

a. The ways that this can be done, if the order of the choices is relevant is 30240 ways

b. The ways that this is done if the order of the choices is not relevant is 252 ways.

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

In this case, the ways that this can be done, if the order of the choices is relevant is:

= ¹⁰P₅

= 10! / (10 - 5)!

= 10 × 9 × 8 × 7 × 6

= 30240 ways

b. The ways that this is done if the order of the choices is not relevant is:

= ¹⁰C₅

= 10! / (10 - 5)! 5!

= 10 × 9 × 8 × 7 × 6 / 5 × 4 × 3 × 2

= 252 ways

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